Each is subdivided into other variants listed below. Note that although the unit cell in these crystals is conventionally taken to be a cube, the primitive unit cell often is not. This is related to the fact that in most cubic crystal systems, there is more than one atom per cubic unit cell.

The primitive cubic system (cP) consists of one lattice point on each corner of the cube. Each atom at a lattice point is then shared equally between eight adjacent cubes, and the unit cell therefore contains in total one atom (1⁄8 × 8).
The body-centered cubic system (cI) has one lattice point in the center of the unit cell in addition to the eight corner points. It has a net total of 2 lattice points per unit cell (1⁄8 × 8 + 1).
The face-centered cubic system (cF) has lattice points on the faces of the cube, that each gives exactly one half contribution, in addition to the corner lattice points, giving a total of 4 lattice points per unit cell (1⁄8 × 8 from the corners plus 1⁄2 × 6 from the faces). Each sphere in a cF lattice has coordination number 12.

The face-centered cubic system is closely related to the hexagonal close packed (HCP) system, and the two systems differ only in the relative placements of their hexagonal layers. The [111] plane of a face-centered cubic system is a hexagonal grid.

Attempting to create a C-centered cubic crystal system (i.e., putting an extra lattice point in the center of each horizontal face) would result in a simple tetragonalBravais lattice.

A body-centered cubic unit cell has six octahedral voids located at the center of each face of the unit cell, for a total of three net octahedral voids. Additionally, there are 36 tetrahedral voids located in an octahedral spacing around each octahedral void, for a total of eighteen net tetrahedral voids. These tetrahedral voids are not local maxima and are not technically voids, but they do occasionally appear in multi-atom unit cells.

A face-centered cubic unit cell has eight tetrahedral voids located slightly towards the center from each corner of the unit cell, for a total of eight net tetrahedral voids. Additionally, there are twelve octahedral voids located at the center of edge of the unit cell as well as one octahedral hole in the very center, for a total of four net octahedral voids.

One important characteristic of a crystalline structure is its atomic packing factor. This is calculated by assuming that all the atoms are identical spheres, with a radius large enough that each sphere abuts the next. The atomic packing factor is the proportion of space filled by these spheres.

Assuming one atom per lattice point, in a primitive cubic lattice with cube side length a, the sphere radius would be a⁄2 and the atomic packing factor turns out to be about 0.524 (which is quite low). Similarly, in a bcc lattice, the atomic packing factor is 0.680, and in fcc it is 0.740. The fcc value is the highest theoretically possible value for any lattice, although there are other lattices which also achieve the same value, such as hexagonal close packed and one version of tetrahedral bcc.

As a rule, since atoms in a solid attract each other, the more tightly packed arrangements of atoms tend to be more common. (Loosely packed arrangements do occur, though, for example if the orbital hybridization demands certain bond angles.) Accordingly, the primitive-cubic structure, with especially low atomic packing factor, is rare in nature, but is found in polonium.[4][5] The bcc and fcc, with their higher densities, are both quite common in nature. Examples of bcc include iron, chromium, tungsten, and niobium. Examples of fcc include aluminum, copper, gold and silver.

One structure is the "interpenetrating primitive cubic" structure, also called the "cesium chloride" structure. Each of the two atom types forms a separate primitive cubic lattice, with an atom of one type at the center of each cube of the other type. Altogether, the arrangement of atoms is the same as body-centered cubic, but with alternating types of atoms at the different lattice sites. (See picture here.) Alternately, one could view this lattice as a simple cubic structure with a secondary atom in its cubic void.

In addition to cesium chloride itself, the structure also appears in certain other alkali halides when prepared at low temperatures or high pressures.[7] Generally, this structure is more likely to be formed from two elements whose ions are of roughly the same size (for example, ionic radius of Cs+ = 167 pm, and Cl− = 181 pm).

The coordination number of each atom in the structure is 8: the central cation is coordinated to 8 anions on the corners of a cube as shown, and similarly, the central anion is coordinated to 8 cations on the corners of a cube.

The rock-salt crystal structure. Each atom has six nearest neighbors, with octahedral geometry.

The space group of the rock-salt (NaCl) structure is called Fm3m (in Hermann–Mauguin notation), or "225" (in the International Tables for Crystallography). The Strukturbericht designation is "B1".[8]

In the rock-salt or sodium chloride (halite) structure, each of the two atom types forms a separate face-centered cubic lattice, with the two lattices interpenetrating so as to form a 3D checkerboard pattern. (See picture here.) Alternately, one could view this structure as a face-centered cubic structure with secondary atoms in its octahedral holes.

Examples of compounds with this structure include sodium chloride itself, along with almost all other alkali halides, and "many divalent metal oxides, sulfides, selenides, and tellurides".[7] More generally, this structure is more likely to be formed if the cation is somewhat smaller than the anion (a cation/anion radius ratio of 0.414 to 0.732).

The coordination number of each atom in this structure is 6: each cation is coordinated to 6 anions at the vertices of an octahedron, and similarly, each anion is coordinated to 6 cations at the vertices of an octahedron.

The Zincblende structure (also written "zinc blende") is named after the mineral zincblende (sphalerite), one form of zinc sulfide (β-ZnS). As in the rock-salt structure, the two atom types form two interpenetrating face-centered cubic lattices. However, it differs from rock-salt structure in how the two lattices are positioned relative to one another. The zincblende structure has tetrahedralcoordination: Each atom's nearest neighbors consist of four atoms of the opposite type, positioned like the four vertices of a regular tetrahedron. Altogether, the arrangement of atoms in zincblende structure is the same as diamond cubic structure, but with alternating types of atoms at the different lattice sites. (See picture here.)